Have you thought about contacting rental agencies and having an agent find you a rental home in your price range that does allow your dog? My husband and I were trying to move to Missouri from Michigan a few years ago. We Googled rental agencies, spoke with a few agents over the phone, gave them our price limit, number of bedrooms and bathrooms we needed, time limit, and explained we would need a landlord that allowed our dogs. We had a few housing options emailed to us with photo's within hours. If you already have employment in your new state, Google a map of the surrounding areas. Then Google newspapers in that area. Check the newspapers for rental homes and look for available properties that suit your needs. Make calls to landlords. Also check out Craigslist in the new area for rentals available, too. If that fails, then I am sorry for you and your dog, but failing a responsible home or a great rescue with an opening I would agree with putting the dog down.